The topological edge states of two-dimensional topological insulators with large energy gap furnish ideal conduction channels for dissipationless current transport. Transition metal tellurides XTe5 (X=Zr, Hf) are theoretically predicted to be large-gap two-dimensional topological insulators and the experimental observations of their bulk insulating gap and in-gap edge states have been reported, but the topological nature of these edge states still remains to be further elucidated. Here, we report our low temperature scanning tunneling microscopy/spectroscopy study on single crystals of HfTe5. We demonstrate a full energy gap of ~80 meV near the Fermi level on the surface monolayer of HfTe5 and that such insulating energy gap gets filled with finite energy states when measured at the monolayer step edges. Remarkably, such states are absent at the edges of a narrow monolayer strip of one-unit-cell in width but persist at both step edges of a unit-cell wide monolayer groove. These experimental observations strongly indicate that the edge states of HfTe5 monolayers are not trivially caused by translational symmetry breaking, instead they are topological in nature protected by the 2D nontrivial bulk properties.
One-dimensional (1D) gapless hinge states are predicated in the three-dimensional (3D) higher-order topological insulators and topological semimetals, because of the higher-order bulk-boundary correspondence. Nevertheless, the topologically protected property of the hinge states is still not demonstrated so far, because it is not accessible by conventional methods, such as spectroscopy experiments and quantum oscillations. Here, we reveal the topological nature of hinge states in the higher-order topological semimetal Cd3As2 nanoplate through spin potentiometric measurements. The results of cu…
In addition to novel surface states, topological insulators can also exhibit robust gapless states at crystalline defects. Step edges constitute a class of common defects on the surface of crystals. In this work we establish the topological nature of one-dimensional (1D) bound states localized at step edges of the [001] surface of a topological crystalline insulator (TCI) Pb$_{0.7}$Sn$_{0.3}$Se, both theoretically and experimentally. We show that the topological stability of the step edge states arises from an emergent particle-hole symmetry of the surface low-energy physics, and demonstrate t…
Massless Dirac electrons in condensed matter have attracted considerable attention. Unlike conventional electrons, Dirac electrons are described in the form of two-component wave functions. In the surface state of topological insulators, these two components are associated with the spin degrees of freedom, hence governing the magnetic properties. Therefore, the observation of the two-component wave function provides a useful clue for exploring the novel spin phenomena. Here we show that the two-component nature is manifested in the Landau levels (LLs) whose degeneracy is lifted by a Coulomb po…
We demonstrate by high resolution low temperature electron energy loss spectroscopy (EELS) measurements that the long range ferromagnetic (FM) order in vanadium (V)-doped topological insulator Sb$_2$Te$_3$ has the nature of van Vleck-type ferromagnetism. The positions and the relative amplitudes of two core-level peaks (L$_3$ and L$_2$) of the V EELS spectrum show unambiguous change when the sample is cooled from room temperature to T=10K. Magnetotransport and comparison of the measured and simulated EELS spectra confirm that these changes originate from onset of FM order. Crystal field analys…
Identification and control of topological phases in topological thin films offer great opportunity for fundamental research and the fabrication of topology-based devices. Here, combining molecular beam epitaxy, angle-resolved photoemission spectroscopy and ab-initio calculations, we investigate the electronic structure evolution in (Bi1-xInx)2Se3 films with thickness from 2 to 13 quintuple layers. We identify several phases with their characteristic topological nature and evolution between them, i.e., dimensional crossover from a three-dimensional topological insulator with gapless surface sta…
Resonant spin dynamics of topological spin textures are correlated with their topological nature, which can be employed to understand this nature. In this study, we present resonant spin dynamics of three-dimensional topological spin texture, i.e., Neel and Bloch hopfions. Using micromagnetic simulations, we stabilize Bloch and Neel hopfions with bulk and interfacial Dzyaloshinskii-Moriya interaction (DMI), respectively. We identify the ground state spin configuration of both hopfions, effects of anisotropies, geometric confinements, and demagnetizing fields. To confirm topological nature, Hop…
We provide a topological understanding on phonon Hall effect in dielectrics with Raman spinphonon coupling. A general expression for phonon Hall conductivity is obtained in terms of the Berry curvature of band structures. We find a nonmonotonic behavior of phonon Hall conductivity as a function of magnetic field. Moreover, we observe a phase transition in phonon Hall effect, which corresponds to the sudden change of band topology, characterized by the altering of integer Chern numbers. This can be explained by touching and splitting of phonon bands.
We report on angle resolved photoemission spectroscopic studies on a parent topological insulator (TI), Bi$_2$Se$_3$. The line width of the spectral function (inverse of the quasi-particle lifetime) of the topological metallic (TM) states shows an anomalous behavior. This behavior can be reasonably accounted for by assuming decay of the quasi-particles predominantly into bulk electronic states through electron-electron interaction and defect scattering. Studies on aged surfaces reveal that topological metallic states are very much unaffected by the potentials created by adsorbed atoms or molec…
Topological materials with both insulating and semimetal phases can be protected by crystalline (e.g. mirror) symmetry. The insulating phase, called topological crystalline insulator (TCI), has been intensively investigated and observed in three-dimensional materials. However, the predicted two-dimensional (2D) materials with TCI phase are explored much less than 3D TCIs and 2D topological insulator, while so far considered 2D TCIs almost exclusively possess a square lattice structure with the mirror Chern number $\mathcal C_{M} =-2$. Here, we predict theoretically that hexagonal monolayer of …
Crystalline $\rm Bi_2Se_3$ is one of the most explored three-dimensional topological insulator, with a $0.3\;\rm eV$ energy gap making it promising for applications. Its amorphous counterpart could bring to light new possibilities for large scale synthesis and applications. Using ab initio molecular dynamics simulations, we have studied realistic amorphous $\rm Bi_2Se_3$ phases generated by different processes of melting, quenching, and annealing. Extensive structural and electronic characterizations show that the melting process induces an energy gap decrease ruled by growth of the defective …
The discovery of three-dimensional (3D) topological insulators opens a gateway to generate unusual phases and particles made of the helical surface electrons, proposing new applications using unusual spin nature. Demonstration of the helical electron transport is a crucial step to both physics and device applications of topological insulators. Topological insulator nanowires, of which spin-textured surface electrons form 1D band manipulated by enclosed magnetic flux, offer a unique nanoscale platform to realize quantum transport of spin-momentum locking nature. Here, we report an observation o…
We report a new type of phononic crystals with topologically non-trivial bandgaps for both longitudinal and transverse polarizations, resulting in protected one-way elastic edge waves. In our design, gyroscopic inertial effects are used to break the time-reversal symmetry and realize the phononic analogue of the electronic quantum Hall effect. We investigate the response of both hexagonal and square gyroscopic lattices and observe bulk Chern number of 1 and 2, indicating that these structures support single and multi-mode edge elastic waves immune to back-scattering. These robust one-way phono…
We demonstrate the existence of atomically-sized topological solitons in a quasi one-dimensional charge density wave system: indium atomic wires on Si(111). Performing joint scanning tunneling microscopy and density-functional calculations, we show that the Si(111)-(8x2)In surface features two conceptually different types of abrupt phase flip structures. One is caused by In adatoms and is, hence, non-solitonic in nature. The other one is an abrupt left-chiral soliton.
We have performed a systematic high-momentum-resolution photoemission study on ZrTe$_5$ using $6$ eV photon energy. We have measured the band structure near the $Γ$ point, and quantified the gap between the conduction and valence band as $18 \leq Δ\leq 29$ meV. We have also observed photon-energy-dependent behavior attributed to final-state effects and the 3D nature of the material's band structure. Our interpretation indicates the gap is intrinsic and reconciles discrepancies on the existence of a topological surface state reported by different studies. The existence of a gap suggests that Zr…
Dirac semimetal is a class of semi-metallic phase protected by certain types of crystalline symmetries, and its low-energy effective Hamiltonian is described by Dirac equations in three dimensions (3D). Despite of various theoretical studies, theories that describe the topological nature of Dirac semimetals have not been well established. In this work, we define a topological invariant for 3D Dirac semimetals by establishing a mapping between a 3D Dirac semimetal and a topological crystalline insulator in four dimension (4D). We demonstrate this scheme by constructing a tight-binding model for…
Electric polarization or transferred charge due to an adiabatic change of external parameters $\vec{Q}$ is expressed in terms of a vector field defined in the $\vec{Q}$ space. This vector field is characterized by strings, i.e., trajectories of band-crossing points. In particular, the transverse component is given by the Biot-Savart law in a nonlocal way. For a cyclic change of $\vec{Q}$ along a loop C, the linking number between this string and C represents the amount of the pumped charge, which is quantized to be an integer as discussed by Thouless.
National Cheng Kung University（国立成功大学）；Northeastern University（东北大学）；Quantum Materials and Sensing Institute, Northeastern University（东北大学量子材料与传感研究所）；Institute of Physics, Academia Sinica（中央研究院物理研究所）；Center for Quantum Frontiers of Research and Technology (QFort)（量子前沿研究与技术中心）；Physics Division, National Center for Theoretical Sciences（国家理论科学中心物理组）
We present a detailed investigation of the magnetic and structural properties of magnetically doped 3D topological insulator Bi2Se3. From muon spin relaxation measurements in zero magnetic field, we find that even 5% Fe doping on the Bi site turns the full volume of the sample magnetic at temperatures as high as ~250 K. This is also confirmed by magnetization measurements. Two magnetic "phases" are identified; the first is observed between ~10-250 K while the second appears below ~10 K. These cannot be attributed to impurity phases in the samples. We discuss the nature and details of the obser…
The recent discovery of a topological phase transition in IV-VI narrow-gap semiconductors has revitalized the decades-old interest in the bulk band inversion occurring in these materials. Here we systematically study the (001) surface states of Pb{1-x}Sn{x}Se mixed crystals by means of angle-resolved photoelectron spectroscopy in the parameter space 0 <= x <= 0.37 and 300 K >= T >= 9 K. Using the surface-state observations, we monitor directly the topological phase transition in this solid solution and gain valuable information on the evolution of the underlying fundamental band gap of the sys…
We demonstrate, using first-principles calculations, that the electronic structure of FeSe$_{1-x}$Te$_{x}$ ($x$=0.5) is topologically non-trivial, characterized by an odd $\mathbb Z_2$ invariant and Dirac cone type surface states, in sharp contrast to the end member FeSe ($x$=0). This topological state is induced by the enhanced three-dimensionality and spin-orbit coupling due to Te substitution (compared to FeSe), characterized by a band inversion at the $Z$ point of the Brillouin zone, which is confirmed by our ARPES measurements. The results suggest that the surface of FeSe$_{0.5}$Te$_{0.5}…
Recent theoretical studies employing density-functional theory have predicted BaBiO$_{3}$ (when doped with electrons) and YBiO$_{3}$ to become a topological insulator (TI) with a large topological gap (~ 0.7 eV). This, together with the natural stability against surface oxidation, makes the Bismuth-Oxide family of special interest for possible applications in quantum information and spintronics. The central question, we study here, is whether the hole-doped Bismuth Oxides, i.e. Ba$_{1-x}$K$_{x}$BiO$_{3}$ and BaPb$_{1-x}$Bi$_{x}$O$_{3}$, which are "high-Tc" bulk superconducting near 30 K, addit…
It is first observed that the original formulation of the Volterra construction for dislocations and disclinations was related to the role that homotopy plays in strain compatibility, whereas the modern discussions are chiefly concerned with how it relates to the holonomy groups of connections that have non-vanishing torsion and curvature. However, the Saint Venant conditions that follow from assuming infinitesimal strain compatibility imply that both torsion and curvature must vanish. The resolution of the confusion is in the fact that when a manifold is multiply connected a flat connection m…
The topological materials have attracted much attention recently. While three-dimensional topological insulators are becoming abundant, two-dimensional topological insulators remain rare, particularly in natural materials. ZrTe5 has host a long-standing puzzle on its anomalous transport properties; its underlying origin remains elusive. Lately, ZrTe5 has ignited renewed interest because it is predicted that single-layer ZrTe5 is a two-dimensional topological insulator and there is possibly a topological phase transition in bulk ZrTe5. However, the topological nature of ZrTe5 is under debate as…
In this report, we demonstrate that the energy gap in Cr-doped Bi2Se3 closes and reopens in oscillatory fashion with increasing sample thickness indicating the topological quantum phase transition driven by the quantum finite size effect. The pattern of the oscillation provides an evidence that Cr-doped Bi2Se3 can have a Dirac semimetal state depending on the sample thickness and Cr-content. This resolves the puzzle of non-magnetic gap opening at the Dirac point of topological insulators. An energy gap can be opened due to the quantum finite size confinement of the bands in Dirac semimetal sta…
Upon mechanical loading, granular materials yield and undergo plastic deformation. The nature of plastic deformation is essential for the development of the macroscopic constitutive models and the understanding of shear band formation. However, we still do not fully understand the microscopic nature of plastic deformation in disordered granular materials. Here we used synchrotron X-ray tomography technique to track the structural evolutions of three-dimensional granular materials under shear. We establish that highly distorted coplanar tetrahedra are the structural defects responsible for micr…
Modification of the gap at the Dirac point (DP) in antiferromagnetic (AFM) axion topological insulator MnBi$_2$Te$_4$ and its electronic and spin structure has been studied by angle- and spin-resolved photoemission spectroscopy (ARPES) under laser excitation with variation of temperature (9-35~K), light polarization and photon energy. We have distinguished both a large (62-67~meV) and a reduced (15-18~meV) gap at the DP in the ARPES dispersions, which remains open above the Néel temperature ($T_\mathrm{N}=24.5$~K). We propose that the gap above $T_\mathrm{N}$ remains open due to short-range ma…
ZrTe$_5$ and HfTe$_5$ have attracted increasingly attention recently since the theoretical prediction of being topological insulators (TIs). However, subsequent works show many contradictions about their topological nature.Three possible phases, i.e. strong TI, weak TI, and Dirac semi-metal, have been observed in different experiments until now. Essentially whether ZrTe$_5$ or HfTe$_5$ has a band gap or not is still a question. Here, we present detailed first-principles calculations on the electronic and topological properties of ZrTe$_5$ and HfTe$_5$ on variant volumes and clearly demonstrate…
Topological semimetals, including Dirac semimetals, Weyl semimetals, and nodal line semimetals, receive enormous research interest due to their intrinsic topological nature and fascinating properties. In present work, with the help of density functional theory (DFT), we find that nodal line semimetals and Dirac semimetals can coexist in the low energy electron of two dimensional (2D) monolayer B2C. Intriguingly, besides type-I and type-II Dirac fermions, a kind of open nodal line appears around the Fermi level. The low energy electronic nature of B2C sheet can be described by a tight-binding (…
Colloidal particles in liquid crystals tend to induce topological defects and distortions of the molecular alignment within the surrounding anisotropic host medium, which results in elasticity-mediated interactions not accessible to their counterparts within isotropic fluid hosts. Such particle-induced coronae of perturbed nematic order are highly responsive to external electric fields, even when the uniformly aligned host medium away from particles exhibits no response to fields below the realignment threshold. Here we harness the non-reciprocal nature of these facile electric responses to de…
Layered three-dimensional (3D) topological semimetals have attracted intensively attention due to the exotic phenomena and abundantly tunable properties. Here we report the experimental evidence for the 3D topological semimetal phase in layered material TaNiTe5 single crystals through quantum oscillations. Strong quantum oscillations have been observed with diamagnetism background in TaNiTe5. By analyzing the de Haas-van Alphen oscillations, multi-periodic oscillations were extracted, in content with magnetotransport measurements. Moreover, nontrivial "π" Berry phase with 3D Fermi surface is i…
